// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"

// Test the corner cases of pow(x, y) for real types.
template<typename Scalar>
void
pow_test()
{
	const Scalar zero = Scalar(0);
	const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
	const Scalar one = Scalar(1);
	const Scalar two = Scalar(2);
	const Scalar three = Scalar(3);
	const Scalar sqrt_half = Scalar(std::sqrt(0.5));
	const Scalar sqrt2 = Scalar(std::sqrt(2));
	const Scalar inf = Eigen::NumTraits<Scalar>::infinity();
	const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN();
	const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
	const Scalar min = (std::numeric_limits<Scalar>::min)();
	const Scalar max = (std::numeric_limits<Scalar>::max)();
	const Scalar max_exp =
		(static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps;

	const static Scalar abs_vals[] = { zero, denorm_min, min,	  eps, sqrt_half, one, sqrt2,
									   two,	 three,		 max_exp, max, inf,		  nan };
	const int abs_cases = 13;
	const int num_cases = 2 * abs_cases * 2 * abs_cases;
	// Repeat the same value to make sure we hit the vectorized path.
	const int num_repeats = 32;
	Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases);
	Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases);
	int count = 0;
	for (int i = 0; i < abs_cases; ++i) {
		const Scalar abs_x = abs_vals[i];
		for (int sign_x = 0; sign_x < 2; ++sign_x) {
			Scalar x_case = sign_x == 0 ? -abs_x : abs_x;
			for (int j = 0; j < abs_cases; ++j) {
				const Scalar abs_y = abs_vals[j];
				for (int sign_y = 0; sign_y < 2; ++sign_y) {
					Scalar y_case = sign_y == 0 ? -abs_y : abs_y;
					for (int repeat = 0; repeat < num_repeats; ++repeat) {
						x(repeat, count) = x_case;
						y(repeat, count) = y_case;
					}
					++count;
				}
			}
		}
	}

	Array<Scalar, Dynamic, Dynamic> actual = x.pow(y);
	const Scalar tol = test_precision<Scalar>();
	bool all_pass = true;
	for (int i = 0; i < 1; ++i) {
		for (int j = 0; j < num_cases; ++j) {
			Scalar e = static_cast<Scalar>(std::pow(x(i, j), y(i, j)));
			Scalar a = actual(i, j);
			bool fail = !(a == e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e));
			all_pass &= !fail;
			if (fail) {
				std::cout << "pow(" << x(i, j) << "," << y(i, j) << ")   =   " << a << " !=  " << e << std::endl;
			}
		}
	}
	VERIFY(all_pass);
}

template<typename ArrayType>
void
array(const ArrayType& m)
{
	typedef typename ArrayType::Scalar Scalar;
	typedef typename ArrayType::RealScalar RealScalar;
	typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
	typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;

	Index rows = m.rows();
	Index cols = m.cols();

	ArrayType m1 = ArrayType::Random(rows, cols), m2 = ArrayType::Random(rows, cols), m3(rows, cols);
	ArrayType m4 = m1; // copy constructor
	VERIFY_IS_APPROX(m1, m4);

	ColVectorType cv1 = ColVectorType::Random(rows);
	RowVectorType rv1 = RowVectorType::Random(cols);

	Scalar s1 = internal::random<Scalar>(), s2 = internal::random<Scalar>();

	// scalar addition
	VERIFY_IS_APPROX(m1 + s1, s1 + m1);
	VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows, cols, s1) + m1);
	VERIFY_IS_APPROX(s1 - m1, (-m1) + s1);
	VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows, cols, s1));
	VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows, cols, s1) - m1);
	VERIFY_IS_APPROX((m1 * Scalar(2)) - s2, (m1 + m1) - ArrayType::Constant(rows, cols, s2));
	m3 = m1;
	m3 += s2;
	VERIFY_IS_APPROX(m3, m1 + s2);
	m3 = m1;
	m3 -= s1;
	VERIFY_IS_APPROX(m3, m1 - s1);

	// scalar operators via Maps
	m3 = m1;
	ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
	VERIFY_IS_APPROX(m1, m3 - m2);

	m3 = m1;
	ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
	VERIFY_IS_APPROX(m1, m3 + m2);

	m3 = m1;
	ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
	VERIFY_IS_APPROX(m1, m3 * m2);

	m3 = m1;
	m2 = ArrayType::Random(rows, cols);
	m2 = (m2 == 0).select(1, m2);
	ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
	VERIFY_IS_APPROX(m1, m3 / m2);

	// reductions
	VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
	VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
	using std::abs;
	VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
	VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
	if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1 + m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
		VERIFY_IS_NOT_APPROX(((m1 + m2).rowwise().sum()).sum(), m1.sum());
	VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar, Scalar>()));

	// vector-wise ops
	m3 = m1;
	VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
	m3 = m1;
	VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
	m3 = m1;
	VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
	m3 = m1;
	VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);

	// Conversion from scalar
	VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows, cols, s1));
	VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows, cols, 1));
	VERIFY_IS_APPROX((m3.topLeftCorner(rows, cols) = 1), ArrayType::Constant(rows, cols, 1));
	typedef Array<Scalar,
				  ArrayType::RowsAtCompileTime == Dynamic ? 2 : ArrayType::RowsAtCompileTime,
				  ArrayType::ColsAtCompileTime == Dynamic ? 2 : ArrayType::ColsAtCompileTime,
				  ArrayType::Options>
		FixedArrayType;
	{
		FixedArrayType f1(s1);
		VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
		FixedArrayType f2(numext::real(s1));
		VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
		FixedArrayType f3((int)100 * numext::real(s1));
		VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100 * numext::real(s1)));
		f1.setRandom();
		FixedArrayType f4(f1.data());
		VERIFY_IS_APPROX(f4, f1);
	}
#if EIGEN_HAS_CXX11
	{
		FixedArrayType f1{ s1 };
		VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
		FixedArrayType f2{ numext::real(s1) };
		VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
		FixedArrayType f3{ (int)100 * numext::real(s1) };
		VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100 * numext::real(s1)));
		f1.setRandom();
		FixedArrayType f4{ f1.data() };
		VERIFY_IS_APPROX(f4, f1);
	}
#endif

	// pow
	VERIFY_IS_APPROX(m1.pow(2), m1.square());
	VERIFY_IS_APPROX(pow(m1, 2), m1.square());
	VERIFY_IS_APPROX(m1.pow(3), m1.cube());
	VERIFY_IS_APPROX(pow(m1, 3), m1.cube());
	VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
	VERIFY_IS_APPROX(pow(2 * m1, 3), 8 * m1.cube());
	ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
	VERIFY_IS_APPROX(Eigen::pow(m1, exponents), m1.square());
	VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
	VERIFY_IS_APPROX(Eigen::pow(2 * m1, exponents), 4 * m1.square());
	VERIFY_IS_APPROX((2 * m1).pow(exponents), 4 * m1.square());
	VERIFY_IS_APPROX(Eigen::pow(m1, 2 * exponents), m1.square().square());
	VERIFY_IS_APPROX(m1.pow(2 * exponents), m1.square().square());
	VERIFY_IS_APPROX(Eigen::pow(m1(0, 0), exponents), ArrayType::Constant(rows, cols, m1(0, 0) * m1(0, 0)));

	// Check possible conflicts with 1D ctor
	typedef Array<Scalar, Dynamic, 1> OneDArrayType;
	{
		OneDArrayType o1(rows);
		VERIFY(o1.size() == rows);
		OneDArrayType o2(static_cast<int>(rows));
		VERIFY(o2.size() == rows);
	}
#if EIGEN_HAS_CXX11
	{
		OneDArrayType o1{ rows };
		VERIFY(o1.size() == rows);
		OneDArrayType o4{ int(rows) };
		VERIFY(o4.size() == rows);
	}
#endif
	// Check possible conflicts with 2D ctor
	typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType;
	typedef Array<Scalar, 2, 1> ArrayType2;
	{
		TwoDArrayType o1(rows, cols);
		VERIFY(o1.rows() == rows);
		VERIFY(o1.cols() == cols);
		TwoDArrayType o2(static_cast<int>(rows), static_cast<int>(cols));
		VERIFY(o2.rows() == rows);
		VERIFY(o2.cols() == cols);

		ArrayType2 o3(rows, cols);
		VERIFY(o3(0) == Scalar(rows) && o3(1) == Scalar(cols));
		ArrayType2 o4(static_cast<int>(rows), static_cast<int>(cols));
		VERIFY(o4(0) == Scalar(rows) && o4(1) == Scalar(cols));
	}
#if EIGEN_HAS_CXX11
	{
		TwoDArrayType o1{ rows, cols };
		VERIFY(o1.rows() == rows);
		VERIFY(o1.cols() == cols);
		TwoDArrayType o2{ int(rows), int(cols) };
		VERIFY(o2.rows() == rows);
		VERIFY(o2.cols() == cols);

		ArrayType2 o3{ rows, cols };
		VERIFY(o3(0) == Scalar(rows) && o3(1) == Scalar(cols));
		ArrayType2 o4{ int(rows), int(cols) };
		VERIFY(o4(0) == Scalar(rows) && o4(1) == Scalar(cols));
	}
#endif
}

template<typename ArrayType>
void
comparisons(const ArrayType& m)
{
	using std::abs;
	typedef typename ArrayType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	Index rows = m.rows();
	Index cols = m.cols();

	Index r = internal::random<Index>(0, rows - 1), c = internal::random<Index>(0, cols - 1);

	ArrayType m1 = ArrayType::Random(rows, cols), m2 = ArrayType::Random(rows, cols), m3(rows, cols), m4 = m1;

	m4 = (m4.abs() == Scalar(0)).select(1, m4);

	VERIFY(((m1 + Scalar(1)) > m1).all());
	VERIFY(((m1 - Scalar(1)) < m1).all());
	if (rows * cols > 1) {
		m3 = m1;
		m3(r, c) += 1;
		VERIFY(!(m1 < m3).all());
		VERIFY(!(m1 > m3).all());
	}
	VERIFY(!(m1 > m2 && m1 < m2).any());
	VERIFY((m1 <= m2 || m1 >= m2).all());

	// comparisons array to scalar
	VERIFY((m1 != (m1(r, c) + 1)).any());
	VERIFY((m1 > (m1(r, c) - 1)).any());
	VERIFY((m1 < (m1(r, c) + 1)).any());
	VERIFY((m1 == m1(r, c)).any());

	// comparisons scalar to array
	VERIFY(((m1(r, c) + 1) != m1).any());
	VERIFY(((m1(r, c) - 1) < m1).any());
	VERIFY(((m1(r, c) + 1) > m1).any());
	VERIFY((m1(r, c) == m1).any());

	// test Select
	VERIFY_IS_APPROX((m1 < m2).select(m1, m2), m1.cwiseMin(m2));
	VERIFY_IS_APPROX((m1 > m2).select(m1, m2), m1.cwiseMax(m2));
	Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff()) / Scalar(2);
	for (int j = 0; j < cols; ++j)
		for (int i = 0; i < rows; ++i)
			m3(i, j) = abs(m1(i, j)) < mid ? 0 : m1(i, j);
	VERIFY_IS_APPROX((m1.abs() < ArrayType::Constant(rows, cols, mid)).select(ArrayType::Zero(rows, cols), m1), m3);
	// shorter versions:
	VERIFY_IS_APPROX((m1.abs() < ArrayType::Constant(rows, cols, mid)).select(0, m1), m3);
	VERIFY_IS_APPROX((m1.abs() >= ArrayType::Constant(rows, cols, mid)).select(m1, 0), m3);
	// even shorter version:
	VERIFY_IS_APPROX((m1.abs() < mid).select(0, m1), m3);

	// count
	VERIFY(((m1.abs() + 1) > RealScalar(0.1)).count() == rows * cols);

	// and/or
	VERIFY((m1 < RealScalar(0) && m1 > RealScalar(0)).count() == 0);
	VERIFY((m1 < RealScalar(0) || m1 >= RealScalar(0)).count() == rows * cols);
	RealScalar a = m1.abs().mean();
	VERIFY((m1 < -a || m1 > a).count() == (m1.abs() > a).count());

	typedef Array<Index, Dynamic, 1> ArrayOfIndices;

	// TODO allows colwise/rowwise for array
	VERIFY_IS_APPROX(((m1.abs() + 1) > RealScalar(0.1)).colwise().count(),
					 ArrayOfIndices::Constant(cols, rows).transpose());
	VERIFY_IS_APPROX(((m1.abs() + 1) > RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
}

template<typename ArrayType>
void
array_real(const ArrayType& m)
{
	using std::abs;
	using std::sqrt;
	typedef typename ArrayType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	Index rows = m.rows();
	Index cols = m.cols();

	ArrayType m1 = ArrayType::Random(rows, cols), m2 = ArrayType::Random(rows, cols), m3(rows, cols), m4 = m1;

	m4 = (m4.abs() == Scalar(0)).select(Scalar(1), m4);

	Scalar s1 = internal::random<Scalar>();

	// these tests are mostly to check possible compilation issues with free-functions.
	VERIFY_IS_APPROX(m1.sin(), sin(m1));
	VERIFY_IS_APPROX(m1.cos(), cos(m1));
	VERIFY_IS_APPROX(m1.tan(), tan(m1));
	VERIFY_IS_APPROX(m1.asin(), asin(m1));
	VERIFY_IS_APPROX(m1.acos(), acos(m1));
	VERIFY_IS_APPROX(m1.atan(), atan(m1));
	VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
	VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
	VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
#if EIGEN_HAS_CXX11_MATH
	VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1)));
	VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1)));
	VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1)));
#endif
	VERIFY_IS_APPROX(m1.logistic(), logistic(m1));

	VERIFY_IS_APPROX(m1.arg(), arg(m1));
	VERIFY_IS_APPROX(m1.round(), round(m1));
	VERIFY_IS_APPROX(m1.rint(), rint(m1));
	VERIFY_IS_APPROX(m1.floor(), floor(m1));
	VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
	VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
	VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
	VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
	VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
	VERIFY_IS_APPROX(m1.abs(), abs(m1));
	VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
	VERIFY_IS_APPROX(m1.square(), square(m1));
	VERIFY_IS_APPROX(m1.cube(), cube(m1));
	VERIFY_IS_APPROX(cos(m1 + RealScalar(3) * m2), cos((m1 + RealScalar(3) * m2).eval()));
	VERIFY_IS_APPROX(m1.sign(), sign(m1));
	VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all());

	// avoid inf and NaNs so verification doesn't fail
	m3 = m4.abs();
	VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3)));
	VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1) / sqrt(abs(m3)));
	VERIFY_IS_APPROX(rsqrt(m3), Scalar(1) / sqrt(abs(m3)));
	VERIFY_IS_APPROX(m3.log(), log(m3));
	VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
	VERIFY_IS_APPROX(m3.log10(), log10(m3));
	VERIFY_IS_APPROX(m3.log2(), log2(m3));

	VERIFY((!(m1 > m2) == (m1 <= m2)).all());

	VERIFY_IS_APPROX(sin(m1.asin()), m1);
	VERIFY_IS_APPROX(cos(m1.acos()), m1);
	VERIFY_IS_APPROX(tan(m1.atan()), m1);
	VERIFY_IS_APPROX(sinh(m1), Scalar(0.5) * (exp(m1) - exp(-m1)));
	VERIFY_IS_APPROX(cosh(m1), Scalar(0.5) * (exp(m1) + exp(-m1)));
	VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5) * (exp(m1) - exp(-m1))) / (Scalar(0.5) * (exp(m1) + exp(-m1))));
	VERIFY_IS_APPROX(logistic(m1), (Scalar(1) / (Scalar(1) + exp(-m1))));
	VERIFY_IS_APPROX(arg(m1), ((m1 < Scalar(0)).template cast<Scalar>()) * Scalar(std::acos(Scalar(-1))));
	VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
	VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all());
	VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all());
	VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all());
	VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all());
	VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all());
	VERIFY((Eigen::isnan)((m1 * Scalar(0)) / Scalar(0)).all());
	VERIFY((Eigen::isinf)(m4 / Scalar(0)).all());
	VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1 * Scalar(0) / Scalar(0))) &&
			(!(Eigen::isfinite)(m4 / Scalar(0))))
			   .all());
	VERIFY_IS_APPROX(inverse(inverse(m4)), m4);
	VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
	VERIFY_IS_APPROX(m3, sqrt(abs2(m3)));
	VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - m1));
	VERIFY_IS_APPROX(m1.sign(), -(-m1).sign());
	VERIFY_IS_APPROX(m1 * m1.sign(), m1.abs());
	VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);

	VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
	VERIFY_IS_APPROX(numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)), numext::abs2(m1));
	if (!NumTraits<Scalar>::IsComplex)
		VERIFY_IS_APPROX(numext::real(m1), m1);

	// shift argument of logarithm so that it is not zero
	Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
	VERIFY_IS_APPROX((m3 + smallNumber).log(), log(abs(m3) + smallNumber));
	VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log(), log1p(abs(m3) + smallNumber));

	VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1 + m2));
	VERIFY_IS_APPROX(m1.exp(), exp(m1));
	VERIFY_IS_APPROX(m1.exp() / m2.exp(), (m1 - m2).exp());

	VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
	VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber));

	VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
	VERIFY_IS_APPROX(pow(m3, RealScalar(0.5)), m3.sqrt());

	VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
	VERIFY_IS_APPROX(pow(m3, RealScalar(-0.5)), m3.rsqrt());

	// Avoid inf and NaN.
	m3 = (m1.square() < NumTraits<Scalar>::epsilon()).select(Scalar(1), m3);
	VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
	pow_test<Scalar>();

	VERIFY_IS_APPROX(log10(m3), log(m3) / numext::log(Scalar(10)));
	VERIFY_IS_APPROX(log2(m3), log(m3) / numext::log(Scalar(2)));

	// scalar by array division
	const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
	s1 += Scalar(tiny);
	m1 += ArrayType::Constant(rows, cols, Scalar(tiny));
	VERIFY_IS_APPROX(s1 / m1, s1 * m1.inverse());

	// check inplace transpose
	m3 = m1;
	m3.transposeInPlace();
	VERIFY_IS_APPROX(m3, m1.transpose());
	m3.transposeInPlace();
	VERIFY_IS_APPROX(m3, m1);
}

template<typename ArrayType>
void
array_complex(const ArrayType& m)
{
	typedef typename ArrayType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	Index rows = m.rows();
	Index cols = m.cols();

	ArrayType m1 = ArrayType::Random(rows, cols), m2(rows, cols), m4 = m1;

	m4.real() = (m4.real().abs() == RealScalar(0)).select(RealScalar(1), m4.real());
	m4.imag() = (m4.imag().abs() == RealScalar(0)).select(RealScalar(1), m4.imag());

	Array<RealScalar, -1, -1> m3(rows, cols);

	for (Index i = 0; i < m.rows(); ++i)
		for (Index j = 0; j < m.cols(); ++j)
			m2(i, j) = sqrt(m1(i, j));

	// these tests are mostly to check possible compilation issues with free-functions.
	VERIFY_IS_APPROX(m1.sin(), sin(m1));
	VERIFY_IS_APPROX(m1.cos(), cos(m1));
	VERIFY_IS_APPROX(m1.tan(), tan(m1));
	VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
	VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
	VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
	VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
	VERIFY_IS_APPROX(m1.arg(), arg(m1));
	VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
	VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
	VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
	VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
	VERIFY_IS_APPROX(m1.log(), log(m1));
	VERIFY_IS_APPROX(m1.log10(), log10(m1));
	VERIFY_IS_APPROX(m1.log2(), log2(m1));
	VERIFY_IS_APPROX(m1.abs(), abs(m1));
	VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
	VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
	VERIFY_IS_APPROX(m1.square(), square(m1));
	VERIFY_IS_APPROX(m1.cube(), cube(m1));
	VERIFY_IS_APPROX(cos(m1 + RealScalar(3) * m2), cos((m1 + RealScalar(3) * m2).eval()));
	VERIFY_IS_APPROX(m1.sign(), sign(m1));

	VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1 + m2));
	VERIFY_IS_APPROX(m1.exp(), exp(m1));
	VERIFY_IS_APPROX(m1.exp() / m2.exp(), (m1 - m2).exp());

	VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
	VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.);
	// Check for larger magnitude complex numbers that expm1 matches exp - 1.
	VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.);

	VERIFY_IS_APPROX(sinh(m1), 0.5 * (exp(m1) - exp(-m1)));
	VERIFY_IS_APPROX(cosh(m1), 0.5 * (exp(m1) + exp(-m1)));
	VERIFY_IS_APPROX(tanh(m1), (0.5 * (exp(m1) - exp(-m1))) / (0.5 * (exp(m1) + exp(-m1))));
	VERIFY_IS_APPROX(logistic(m1), (1.0 / (1.0 + exp(-m1))));

	for (Index i = 0; i < m.rows(); ++i)
		for (Index j = 0; j < m.cols(); ++j)
			m3(i, j) = std::atan2(m1(i, j).imag(), m1(i, j).real());
	VERIFY_IS_APPROX(arg(m1), m3);

	std::complex<RealScalar> zero(0.0, 0.0);
	VERIFY((Eigen::isnan)(m1 * zero / zero).all());
#if EIGEN_COMP_MSVC
	// msvc complex division is not robust
	VERIFY((Eigen::isinf)(m4 / RealScalar(0)).all());
#else
#if EIGEN_COMP_CLANG
	// clang's complex division is notoriously broken too
	if ((numext::isinf)(m4(0, 0) / RealScalar(0))) {
#endif
		VERIFY((Eigen::isinf)(m4 / zero).all());
#if EIGEN_COMP_CLANG
	} else {
		VERIFY((Eigen::isinf)(m4.real() / zero.real()).all());
	}
#endif
#endif // MSVC

	VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1 * zero / zero)) && (!(Eigen::isfinite)(m1 / zero))).all());

	VERIFY_IS_APPROX(inverse(inverse(m4)), m4);
	VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
	VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real()) + square(m1.imag())));
	VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
	VERIFY_IS_APPROX(log10(m1), log(m1) / log(10));
	VERIFY_IS_APPROX(log2(m1), log(m1) / log(2));

	VERIFY_IS_APPROX(m1.sign(), -(-m1).sign());
	VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);

	// scalar by array division
	Scalar s1 = internal::random<Scalar>();
	const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
	s1 += Scalar(tiny);
	m1 += ArrayType::Constant(rows, cols, Scalar(tiny));
	VERIFY_IS_APPROX(s1 / m1, s1 * m1.inverse());

	// check inplace transpose
	m2 = m1;
	m2.transposeInPlace();
	VERIFY_IS_APPROX(m2, m1.transpose());
	m2.transposeInPlace();
	VERIFY_IS_APPROX(m2, m1);
	// Check vectorized inplace transpose.
	ArrayType m5 = ArrayType::Random(131, 131);
	ArrayType m6 = m5;
	m6.transposeInPlace();
	VERIFY_IS_APPROX(m6, m5.transpose());
}

template<typename ArrayType>
void
min_max(const ArrayType& m)
{
	typedef typename ArrayType::Scalar Scalar;

	Index rows = m.rows();
	Index cols = m.cols();

	ArrayType m1 = ArrayType::Random(rows, cols);

	// min/max with array
	Scalar maxM1 = m1.maxCoeff();
	Scalar minM1 = m1.minCoeff();

	VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, minM1), (m1.min)(ArrayType::Constant(rows, cols, minM1)));
	VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows, cols, maxM1)));

	VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, maxM1), (m1.max)(ArrayType::Constant(rows, cols, maxM1)));
	VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows, cols, minM1)));

	// min/max with scalar input
	VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, minM1), (m1.min)(minM1));
	VERIFY_IS_APPROX(m1, (m1.min)(maxM1));

	VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, maxM1), (m1.max)(maxM1));
	VERIFY_IS_APPROX(m1, (m1.max)(minM1));

	// min/max with various NaN propagation options.
	if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) {
		m1(0, 0) = NumTraits<Scalar>::quiet_NaN();
		maxM1 = m1.template maxCoeff<PropagateNaN>();
		minM1 = m1.template minCoeff<PropagateNaN>();
		VERIFY((numext::isnan)(maxM1));
		VERIFY((numext::isnan)(minM1));

		maxM1 = m1.template maxCoeff<PropagateNumbers>();
		minM1 = m1.template minCoeff<PropagateNumbers>();
		VERIFY(!(numext::isnan)(maxM1));
		VERIFY(!(numext::isnan)(minM1));
	}
}

template<int N>
struct shift_left
{
	template<typename Scalar>
	Scalar operator()(const Scalar& v) const
	{
		return v << N;
	}
};

template<int N>
struct arithmetic_shift_right
{
	template<typename Scalar>
	Scalar operator()(const Scalar& v) const
	{
		return v >> N;
	}
};

template<typename ArrayType>
void
array_integer(const ArrayType& m)
{
	Index rows = m.rows();
	Index cols = m.cols();

	ArrayType m1 = ArrayType::Random(rows, cols), m2(rows, cols);

	m2 = m1.template shiftLeft<2>();
	VERIFY((m2 == m1.unaryExpr(shift_left<2>())).all());
	m2 = m1.template shiftLeft<9>();
	VERIFY((m2 == m1.unaryExpr(shift_left<9>())).all());

	m2 = m1.template shiftRight<2>();
	VERIFY((m2 == m1.unaryExpr(arithmetic_shift_right<2>())).all());
	m2 = m1.template shiftRight<9>();
	VERIFY((m2 == m1.unaryExpr(arithmetic_shift_right<9>())).all());
}

EIGEN_DECLARE_TEST(array_cwise)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(array(Array<float, 1, 1>()));
		CALL_SUBTEST_2(array(Array22f()));
		CALL_SUBTEST_3(array(Array44d()));
		CALL_SUBTEST_4(array(
			ArrayXXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_5(array(
			ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(array(
			ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(array(Array<Index, Dynamic, Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
															internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(array_integer(
			ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(array_integer(Array<Index, Dynamic, Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
																	internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
	}
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(comparisons(Array<float, 1, 1>()));
		CALL_SUBTEST_2(comparisons(Array22f()));
		CALL_SUBTEST_3(comparisons(Array44d()));
		CALL_SUBTEST_5(comparisons(
			ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(comparisons(
			ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
	}
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(min_max(Array<float, 1, 1>()));
		CALL_SUBTEST_2(min_max(Array22f()));
		CALL_SUBTEST_3(min_max(Array44d()));
		CALL_SUBTEST_5(min_max(
			ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(min_max(
			ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
	}
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(array_real(Array<float, 1, 1>()));
		CALL_SUBTEST_2(array_real(Array22f()));
		CALL_SUBTEST_3(array_real(Array44d()));
		CALL_SUBTEST_5(array_real(
			ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_7(array_real(Array<Eigen::half, 32, 32>()));
		CALL_SUBTEST_8(array_real(Array<Eigen::bfloat16, 32, 32>()));
	}
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_4(array_complex(
			ArrayXXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
	}

	VERIFY((internal::is_same<internal::global_math_functions_filtering_base<int>::type, int>::value));
	VERIFY((internal::is_same<internal::global_math_functions_filtering_base<float>::type, float>::value));
	VERIFY(
		(internal::is_same<internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i>>::value));
	typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd> Xpr;
	VERIFY((internal::is_same<internal::global_math_functions_filtering_base<Xpr>::type, ArrayBase<Xpr>>::value));
}
